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The Global Hub for Research, Study, and Networking Devoted to Enterprises in the Emerging Markets
March 2009
CEME Fellows Research Briefing Series — Volume 1, Issue 2
FX-Adjusted Local Currency Spreads
By Jorge A. Chan-Lau1
I. INTRODUCTION
The trend and volatility of the exchange rate as well as the operating environment of domestic
firms are affected by changes in domestic and international economic conditions. As a result, in
the case of local currency denominated loans or fixed income instruments, the premium associated with exchange rate changes, or currency risk premium, and that associated with default risk,
or default risk premium, are not independent from each other. A common practice, however, is
to consider credit risk and market risk, in this case currency risk, as independent sources of risk
and to simply add the corresponding premia. This practice, that overstates the risk premium that
should be charged to the issuer, is partly supported by risk management practices and regulations that require adding up economic capital charges for credit risk and market risk separately.
This paper attempts to improve current practice by proposing a simple rule of thumb, based on
the joint dynamics of exchange rate changes and the spreads of credit default swaps, to determine the level of local currency spreads consistent with foreign currency credit spreads adjusting
for foreign exchange effects. The rule of thumb proposed here could be useful to those engaged
in pricing and investing in local currency-denominated instruments, as well as those interested in
arbitraging price spread differentials between foreign currency and local currency-denominated
instruments. Before presenting the rule of thumb in detail, I discuss the building blocks for determining local currency spreads.
II. LOCAL CURRENCY SPREADS: BUILDING BLOCKS AND INTUITION
From the standpoint of a foreign investor, the risk premium demanded for holding a naked long
position in local currency-denominated loans and/or fixed income securities comprises two major components: a default risk premium and a currency risk premium.
The default risk premium is associated with the event that the borrower may fail to repay its
debt obligations and reflects the loss given default experienced by the lender. This loss depends
on the exposure at default, the recovery rate, and the probability of default of the borrower. The
currency risk premium is associated with future exchange rate changes as the position records
profits or losses depending on the differences between the forward rate locked into the contract
and the realized exchange rate.
The risk premium, in addition, depends on two other sources of risk: convertibility risk and transfer risk. Convertibility risk is associated with the possibility that, upon receipt of the payment, the
lender may not be able to convert the payment to foreign currency. Transfer risk is associated
CEME Fellows Research Briefing Series Vol. 1, No. 2, March 2009
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“FX-Adjusted Local Currency Spreads”
with the possibility that payments cannot be sent out of the country mainly due to capital account restrictions.
Rather than attempting to model convertibility and transfer risks separately, one common practice in industry is
to embed the premia associated to these two sources of risk into the default risk premium. Specifically, the default risk premium can be decomposed into a systematic component and an idiosyncratic, issuer-specific component. This decomposition is consistent with the one-factor default risk model introduced by Vacisek [1987] and
the one-factor Gaussian copula introduced by Li [2000]. As stated by Li, the intuition behind the one-factor Gaussian copula is that the default rate of a group of issuers is dependent on business cycle conditions.
Even though the systematic risk factor, or common factor, is an unobserved latent factor in the models of
Vacisek and Li, it can be identified as macroeconomic risk, or macro risk. Arguably, convertibility risk and transfer
risk are highly correlated with macro risk: as the macroeconomic risk of a country increases, the more likely the
country will impose capital controls and convertibility restrictions to avoid a balance-of-payments crisis. This observation justifies bundling together convertibility and transfer risk into macro risk.
The discussion above can be summarized succinctly in two equations. When measured in foreign currency, the
risk premium of the issuer is priced as a spread over the risk-free or funding costs of the lender:
(1)
Foreign currency spread = macro spread + idiosyncratic spread.
= issuer spread (in foreign currency)
When measured in local currency, the total spread of the issuer is the sum of the issuer spread, in local currency,
plus a currency spread:
(2)
Local currency total spread = issuer spread (in local currency) + currency spread.
What remains to be determined are the currency spread and how to convert the issuer spread in foreign currency to an issuer spread in local currency. In regards to the currency spread, or domestic-foreign interest rate
differential, it can be determined from covered interest rate parity when there are liquid currency forwards and
swaps markets:
rD ,t − rF ,t = f 0 ,t − s 0
(3)
where
rD ,t
and
rF ,t
,
are the t-periods ahead domestic and foreign risk-free interest rates,
s0
ahead forward exchange rate, and
local currency per foreign currency.
f 0 ,t
is the t-periods
is the spot rate. Both the forward and spot rates are measured in units of
In some instances currency swaps and forwards may not be available but secondary markets for local currencydenominated government bonds may exist. The yields of the local currency instruments could serve as proxies
for determining the domestic-foreign interest rate differential directly.2 When market references are not available, practitioners can use joint econometric models of the exchange rate and the forward premium to construct
a synthetic reference yield curve.3 The estimation of the issuer spread in local currency is straight forward once a
local currency yield curve is available by applying cross-currency swap valuation techniques, i.e. i.e. discounting
the cash flows with the discount factors in each currency and ensuring that it is a zero-value transaction at inception.
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“FX-Adjusted Local Currency Spreads”
What is important in this step is to decide what fraction of currency spread should be added to the local currency
issuer spread to avoid double counting if the currency risk and the macro risk are not independent. A conservative approach is to assume both sources of risk are independent and to add 100 percent of the currency spread
but this may overstate the total risk premium. The correct way to adjust for the dependence between the default risk of the issuer and the currency risk is to incorporate foreign exchange effects in otherwise standard default models. Some of these models are reviewed next. Because calibrating the models to real applications could
be relatively difficult due to the lack of data, the paper then presents a quick-and-dirty way to determine what
fraction of the foreign currency spread should be converted to local currency.4
III. THE CORRECT WAY TO ADJUST DEFAULT RISK FOR FOREIGN EXCHANGE EFFECTS
The literature and availability of default risk models have witnessed an explosive growth driven partly by the
rapid expansion of the credit derivatives market since the early 2000s. Default risk models can be divided into
two main categories, structural models and reduced form models. Structural models link the analysis of the capital structure of the issuer to option pricing theory. Under absolute priority rules, equity shareholders are residual
claimants on the assets of the firm since bondholders are paid first. Thus, equity shareholders are holding a call
option on the assets of the firm, where the strike price is equal to the debt owed to bondholders. Similarly, the
value of the debt owed by the firm is equivalent to a default-free bond plus a short position on a put option on
the assets of the firm.
Warnes and Acosta [2002], Chan-Lau and Santos [2006] and Tasche [2007] are examples of structural default
models that attempt to incorporate currency risk into structural models of default risk. Warnes and Acosta extend the Merton [1974] model to incorporate foreign currency-denominated debt, and under the assumption of
constant interest rates, find closed-form solutions for debt prices. Chan-Lau and Santos [2006] propose a number of default-at-maturity and first-time passage models that allow a mix of foreign and domestic currency liabilities and different assumptions on the stochastic process governing the dynamics of the exchange rate. Tasche
[2007] extends the Merton model to incorporate currency risk by combining it with the foreign exchange option
pricing of Garman and Kohlhagen [1983], and also address the issue of asset correlation among different issuers
by incorporating elements from the model of Vacisek [2002].
In reduced form models, also known as intensity-based models and first introduced by Jarrow and Turnbull
[1995] and Duffie and Singleton [1997], the time of default is determined by an exogenous stochastic process.
The default event is not linked to any observable characteristic of the firm analyzed, which raises questions on
how to identify the drivers of default risk in these models. Along this line of work, Ehlers and Schonbucher [2007]
introduced an affine-jump diffusion default risk model where there exists correlation between the default intensity and the exchange rate, and where the exchange rate is allowed to jump.
IV. THE QUICK-AND-DIRTY WAY TO ADJUST DEFAULT RISK FOR FOREIGN EXCHANGE EFFECTS
The nonlinear relationship between currency risk and macro risk
One common characteristic of the models described in the previous section is that their calibration is rather
complex and long time series data are needed. Another common feature of these models is that there is a linear
dependence between default rates and the exchange rate, modeled by assuming that the diffusions are correlated.
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“FX-Adjusted Local Currency Spreads”
Assuming that default rates and exchange rates are linearly dependent appears at odds with the empirical evidence collected on foreign exchange market microstructure studies. At the risk of oversimplification, exchange
rate determinants are classified broadly into two categories: fundamental factors and technical factors. Business
cycle and economic indicators fall into the first category. Technical trading rules and order flow indicators fall
into the second category.5
Fundamental variables account for very little of the observed variation in exchange rates for developed countries’ currencies over short-time horizons up to one year.6 Dealers’ order flows rather than economic fundamentals are the dominant drivers of exchange rates [Lyons, 2001]. While order flows may aggregate investors’ information about the fundamental drivers of the exchange rate, they also reflect technical effects such as bandwagon effects due to the extrapolative expectations of investors in the short-run [Rosenberg, 2003].
DeGrauwe [1996] points out that the fundamental-based value of a currency cannot be known with certainty.
Therefore, when the exchange rate is within certain range roughly consistent with fundamentals, or within a
“band of agnosticism,” technical factors are the main drivers of exchange rate movements. When macro risk is
low there is not much uncertainty about the fundamentals so the “band of agnosticism” is relatively stable, currency risk and macro risk are relatively independent from each other.
Whenever the exchange rate moves outside the band of agnosticism fundamentals-based investors have an incentive to take positions in the market. But taking positions is costly since it is difficult to assess how long it will
take for the exchange rate to converge to its fundamentals-based value.7 Such position taking, however, becomes less risky the greater the divergence is between the exchange rate and its fundamentals-based value, a
situation typically display by countries vulnerable to a balance-of-payment crisis. As a result, when economic fundamentals are undergoing rapid deterioration they play a bigger role on exchange rate movements. Macro risk
and currency risk, then, become highly dependent on each other.
Since the default risk of an issuer has been decomposed into a systematic component, macro risk, driven by fundamentals, and an idiosyncratic component, it follows that the non-linear relationship between macro risk and
currency risk translates into a similar relationship between default risk and currency risk at the issuer level.
A Variance Decomposition-Based Rule of Thumb
In summary, the nonlinear dependence between macro risk, a major component of default risk, and currency
risk, suggests that adjusting default risk (spreads) for foreign exchange effects needs to account for the level of
macro risk. The rule of thumb proposed here captures this nonlinear dependence.
The rule builds upon a variance decomposition of a bivariate vector autoregression that includes as endogenous
variables exchange rate and macro risk percentage changes. The variance decomposition permits assessing what
percentage of the exchange rate variance is explained by changes in macro risk. When we perform the variance
decomposition on a sample of emerging market countries, a simple relationship that relates the fraction of exchange rate variance explained by macro risk to the level of macro risk emerges.
The monthly data used in the analysis covers the period October 2000 – November 2007. Mid-quotes for 5-year
credit default swap (CDS) contracts and exchange rates were obtained from Bloomberg LP. CDSs are proxies for
macro risk or sovereign default risk. The countries included in the analysis are Argentina, Brazil, Chile, Colombia,
Mexico and Peru in Latin America, Indonesia, South Korea, Malaysia, the Philippines and Thailand in Asia, and
Bulgaria, Kazakhstan, Pakistan, Quatar, South Africa, and Turkey in Eastern Europe and Middle East region.
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“FX-Adjusted Local Currency Spreads”
The percentage of the variance in exchange rates explained by changes in macro risk (CDS spreads) is determined using the long-run variance decomposition proposed by Hasbrouck [1991a,b]. Specifically, given the vector of n endogenous variables, Yt=(y1t, y2t,..., ynt)', the corresponding unrestricted VAR system of order p is:
Yt = c + Φ 1Yt −1 + ...Φ pYt − p + ε t
(3)
,
where c is a n-vector of constant terms, Φi (i=1,...,p) are n-by-n coefficient matrices, and
εt is a vector of uncorrelated, independent and identically distributed error terms. The error terms are also serially uncorrelated. Under certain technical conditions,8 the vector autoregression system in equation (1) could be
represented by the following vector moving average representation (VMA):
 y1t  ψ 11 ( L)
 M   M
  
 yit  = ψ i1 ( L)
  
 M   M
 y nt  ψ n1 ( L)
(4)
L
ψ 1i ( L)
L
M
L
 M 
 
ψ in ( L)   ε it 
 
M  M 
ψ nn ( L) ε nt 
M
ψ ii ( L)
L
M
L
ψ 1n ( L)   ε1t 
ψ ni ( L)
L
,
∞
ψ ij = ∑ψ ijk Lk
k =1
where
, i,j=1,...,n are lag operators.
ψ ijk
The coefficient
measures the effect k periods ahead of a unit shock or innovation to variable yj on variable
yi. Therefore, the long-term cumulative impact of variable yj on variable yi can be measured by adding up the coefficients associated with the lag operator
ψ ij ( L )
:
∞
∑ψ ijk
(5)
k =0
= information of yj on yi.
Equation (5) suggests one way to quantify the overall importance of innovations to variable yj for explaining subsequent realizations of variable yi vis-à-vis the other endogenous variables. Specifically, the overall importance of
variable yj is related to the relative share of the variance of variable yi it explains:
2
(6)
 ∞ k 2
 ∑ψ ij  σ ε j
 k =0 
2
n
 ∞ k  2
∑
 ∑ψ im  σ ε m
m =1  k = 0

σ ε2
j
where
is the variance of the innovation to variable yj. Note that the VAR framework does not choose a particular ordering of the variables entering equation (1), and hence it is a statistical description of the dynamic inter-relations between the variables analyzed.9
CEME Fellows Research Briefing Series Vol. 1, No. 2, March 2009
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“FX-Adjusted Local Currency Spreads”
Exhibit 1 presents the results per country and per region, together with some descriptive statistics of the CDS
spreads per country. The percentage of the exchange rate variance explained by the CDS spreads (or macro risk)
appears to be a function of the level of the spreads rather than the standard deviation, or the coefficient of
variation (the ratio of the standard deviation to the mean).
Exhibit 2 captures the relationship between currency risk and macro risk graphically. If Turkey is excluded from
the analysis, the non-linear relationship between macro risk and currency risk is evident from the figure. At low
levels of macro risk, factors other than those affecting macro and sovereign risk explain most of the variance of
the exchange rate. Interestingly, three of the countries where macro risk and currency risk appear to be independent of each other, Chile, Malaysia, and Thailand, were rated investment grade by Fitch Ratings during the
sample period, and a fourth one, Mexico, was upgraded to investment grade in early 2002.
Similarly, when macro risk is high, it explains most of the exchange rate variance. In this case, adding up the default risk and the currency risk will overstate the risk charged to the issuer. The countries where macro risk and
currency risk appear to be coupled are those that have been rated below-investment grade by Fitch Ratings during most of the sample period. One exception is Bulgaria that was upgraded to investment grade in mid-2004.
Turkey is a notable exception: although macro risk is substantially high, the currency risk appears decoupled
from it.
For practical purposes, Exhibit 2 also suggests the following rule-of-thumb for determining what fraction of the
currency risk should be added to an issuer’s default risk:
Percentage of
currency risk
(7)
to be added to
default risk
5 - year CDS spread

100 −
3.50
= 


0
if 5 - year CDS spread < 350 bps
if 5 - year CDS spread > 350 bps
In contrast to the relatively sophisticated models reviewed in section 3, Equation (7) provides a simple way to
adjust default spreads for foreign exchange effects. Therefore, given the default risk of the borrower in foreign
currency, information on the sovereign risk of the home country of the borrower and the local currency yield
curve, investors and lenders can determine the proper spread of a local currency loan or bond. The procedure
for doing so is exactly the same one explained in section 2 above but replacing equation (2) with equation (2’)
below:
(2’)
Local currency total spread = issuer spread (in local currency) +
adjusted currency spread
V. CONCLUSIONS
Changes in domestic and international economic conditions affect the default risk of a firm. These changes, in
turn, affect the exchange rate of the home country of the firm. As a result, if the firm borrows in local currency,
the total risk compensation received by investors should factor in both default risk and currency risk. But these
two sources of risk are not completely independent, so adding them up may be too conservative in some instances.
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“FX-Adjusted Local Currency Spreads”
From a theoretical point of view, the “correct” way to address this problem is to adapt default risk models, either
of the structural or reduced form type, to incorporate default risk. But the calibration of these models could be
relatively difficult given their data requirements. Furthermore, the models need to incorporate the fact that the
dependence between default risk and currency risk, which works through the systematic risk component of default risk, is nonlinear.
In order to address practitioner needs, this paper presents a simple rule of thumb, based on the joint dynamics
of exchange rate changes and the spreads of credit default swaps, to convert foreign-currency denominated
spreads to local currency-denominated spreads. The rule of thumb, while simple, captures the nonlinear dependence between default risk and currency risk, and could be very useful for investors interested in taking local
currency positions or arbitraging the spreads between foreign currency and local currency-denominated spreads.
Exhibit 1. Exchange rate variance explained by CDS spreads (in percent)
CDS spreads (in bps)
Me an
Minimum
Latin A meric a
A rgentina
300
193
Brazil
700
62
Chile
42
13
Colombia
309
77
M exico
132
28
Peru
207
62
Asia
Indonesia
201
99
K orea
46
14
M alaysia
64
13
The Philippines
349
101
Thailand
57
27
EMEA
Bulgaria
185
13
K azakhstan
71
35
Pakistan
250
138
Q atar
26
11
South A fric a
117
25
Turkey
503
123
Source : Bloomberg LP and author's calculations.
Maximum
Standard
deviation
Excha nge ra te
variance explained
by CDS spreads
(in perce nt)
476
3790
160
805
392
571
82
813
38
189
90
117
99.8
100.0
1.4
42.4
1.9
46.4
367
163
180
618
150
74
27
54
151
37
90.4
22.1
3.0
82.9
2.0
698
208
416
39
255
1281
187
29
80
10
67
331
97.5
16.2
84.0
17.8
37.8
8.3
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Jorge Antonio Chan-Lau
“FX-Adjusted Local Currency Spreads”
Per centage of FX variance explained by CDS spread s
Exhibit 2. Exchange Rate Variance Explained by Changes in CDS Spreads vs.
Sovereign CDS Spreads Levels (in percent)
100
90
Br az il
Arg ent i na
Bu lg ar ia
In don esia
Paki st an
80
Th e Phil ippin es
70
60
50
Per u
Col om bi a
40
Sout h Af ri ca
30
Kor ea
20
Qat ar
10
Chi l e
Kaza khsta n
Turk ey
Mal aysi a
Mex ic o
0
Tha il and
0
100
200
300
400
500
600
700
800
CDS spr ead, in bp s (2 000-2007 aver age)
AUTHOR BIOGRAPHY
Jorge Antonio Chan-Lau is a Fellow at the Center for Emerging Market Enterprises, The Fletcher School, Tufts
University. He is also a senior economist at the International Monetary Fund, where he is a lead contributor to analytical and policy work on financial stability, risk modeling and capital markets, areas in which he has
published widely. During 2007-08 he was on leave as a senior financial officer at the IFC, The World Bank Group,
where he managed a frontier markets local currency loan portfolio, for which he designed and implemented the
valuation and economic capital allocation models.
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“FX-Adjusted Local Currency Spreads”
ENDNOTES
1
Contact information: International Monetary Fund, 700 19th St NW, Washington, DC 20431. This paper was
written while the author was affiliated with the International Finance Corporation, the World Bank Group. The
views presented herein are solely those of the author and do not represent those of the IFC, The World Bank
Group, or the IMF.
2
It should be bear in mind, however, that from a funding perspective, the reference rates should correspond to
the funding rates in domestic and foreign currency of the institution conducting the trade. For example, the
funding rates for a U.S.-based AA-rated international bank should be the U.S. Libor and the domestic interbank
lending rate. The latter may not necessarily coincide with the yield of local currency government bonds.
3
For the sake of conciseness, the forward premium is not discussed here. See Engel (1996), Chinn (2007) and
references therein for a comprehensive discussion.
4
Jiang, Jones, Halkett, and Orlandi (2008) is a recent paper that also introduces a simple way to adjust for the
correlation between currency and credit risk.
5
The reader should keep in the background that the default risk of an issuer has been decomposed into a systematic component, macro risk, that is driven by fundamentals, and an idiosyncratic component. The non-linear
relationship between macro risk and currency risk then translates into a similar relationship between default risk
and currency risk.
6
See Evans (2008) and references therein.
7
See Shleifer and Vishny (1997) for an intuitive explanation on why it is difficult to arbitrage price deviations
from fundamentals.
8
Hamilton (1994).
9
While a structural VAR may offer some advantages for interpreting the data, it requires specifying a priori a
causal ordering of the variables which we do not deem appropriate for this study given that there is little justification for imposing a particular ordering.
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